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# node_redundancy¶

node_redundancy(G, nodes=None)[source]

Compute bipartite node redundancy coefficient.

The redundancy coefficient of a node $$v$$ is the fraction of pairs of neighbors of $$v$$ that are both linked to other nodes. In a one-mode projection these nodes would be linked together even if $$v$$ were not there.

$rc(v) = \frac{|\{\{u,w\} \subseteq N(v), \: \exists v' \neq v,\: (v',u) \in E\: \mathrm{and}\: (v',w) \in E\}|}{ \frac{|N(v)|(|N(v)|-1)}{2}}$

where $$N(v)$$ are the neighbors of $$v$$ in $$G$$.

Parameters: G : graph A bipartite graph nodes : list or iterable (optional) Compute redundancy for these nodes. The default is all nodes in G. redundancy : dictionary A dictionary keyed by node with the node redundancy value.

References

 [R167] Latapy, Matthieu, Clémence Magnien, and Nathalie Del Vecchio (2008). Basic notions for the analysis of large two-mode networks. Social Networks 30(1), 31–48.

Examples

>>> from networkx.algorithms import bipartite
>>> G = nx.cycle_graph(4)
>>> rc = bipartite.node_redundancy(G)
>>> rc[0]
1.0


Compute the average redundancy for the graph:

>>> sum(rc.values())/len(G)
1.0


Compute the average redundancy for a set of nodes:

>>> nodes = [0, 2]
>>> sum(rc[n] for n in nodes)/len(nodes)
1.0